Comptes Rendus
no. 5
Probability Theory
A Riemann zeta stochastic process
[Un processus zeta stochastique de Riemann]

Présenté par : Marc Yor

Werner Ehm1
1 Institute for Frontier Areas of Psychology and Mental Health, Wilhelmstr. 3a, 79098 Freiburg, Germany
Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 279-282.

Il est bien connu que pour tout σ>1 la fonction t↦ζ(σ+it)/ζ(σ) représente la fonction caractéristique d'une loi de probabilité infiniment divisible. L'objectif de cette Note est de présenter une construction d'un processus aléatoire possédant ces lois marginales. Des théorèmes limite fonctionnels pour ce « processus zeta » et d'autres processus voisins sont indiqués également.

It is well-known that for every σ>1 the function t↦ζ(σ+it)/ζ(σ) represents the characteristic function of an infinitely divisible probability distribution. The purpose of this Note is to present a construction of a stochastic process having these distributions as its marginals. Functional limit theorems for this ‘zeta process’ and other related processes are also indicated.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.07.023

Werner Ehm 1

1 Institute for Frontier Areas of Psychology and Mental Health, Wilhelmstr. 3a, 79098 Freiburg, Germany 
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Werner Ehm. A Riemann zeta stochastic process. Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 279-282. doi : 10.1016/j.crma.2007.07.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.023/

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  • Satoshi Takanobu A generalization of functional limit theorems on the Riemann zeta process, Osaka Journal of Mathematics, Volume 56 (2019) no. 4, pp. 843-882 | Zbl:1448.60082

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